English

Diagonalization and representation results for nonpositive sesquilinear form measures

Functional Analysis 2015-05-13 v1

Abstract

We study decompositions of operator measures and more general sesquilinear form measures EE into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent EE as a trace class valued measure of bounded variation on a new Hilbert space related to EE. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals.

Keywords

Cite

@article{arxiv.0706.2121,
  title  = {Diagonalization and representation results for nonpositive sesquilinear form measures},
  author = {Tuomas Hytonen and Juha-Pekka Pellonpaa and Kari Ylinen},
  journal= {arXiv preprint arXiv:0706.2121},
  year   = {2015}
}

Comments

J. Math. Anal. Appl., in press